Question

Yg remedi kecuali no 1 :)

Answer 1

2. 4 sin Ф - 4sin² Ф = 1
0 = 4sin² Ф - 4 sinФ + 1
0 = (2sinФ - 1)²
2sinФ = 1
sin Ф = 1/2
sin Ф = sin 30
Ф = 30
tan 30 = (1/3) √3  (D)

3. cos²α / (1 - sin α) - cos² α / (1 + sin α)
= (cos²α (1 + sin α) - cos² α(1 - sin α) / (1 - sin α) (1 + sinα)
= (cos ²α (1 + sin α) - cos² α(1 - sinα) / (1 - sin²α)
= (cos² α (1 + sin α) - cos²α (1 - sin α) / cos² α
= (1 + sin α) - (1 - sinα)
= 2 sin α    (A)

4. tan a = √2 sin β
tan a = sisi tegak / sisi mendatar    (terhadap sudut α)
tan α = √2 sin β / 1
sisi tegak terhadap α = sisi mendatar terhadap β = √2 sin β
sisi mendatar terhadap α = sisi tegak terhadap β = 1
sisi miring = √1² + (√2 sin β)²
                     = √ (1 + 2 sin² β)
sin β = sisi tegak terhadap β / miring
sin ²β = 1² / ( 1 + 2sin²β)
sin²β + 2sin^4 = 1
2 sin^4 β+ sin² β - 1 = 0
(2 sin²β -1) (sin²β + 1) = 0
2 sin ²β = 1      atau sin²β = -1
sin²β = 1/2
sin β = 1/2 √2
sin β = sin 45
β = 45
α = 180 - 90 - 45 = 45
sin α = sin 45 = (1/2)√2
sin²α = (√2 / 2)² = 1/2    (D)

5. f(x) = -2 cos 2x
f (π/3) = -2 cos 2π/3 = -2 cos 120 = -2 (-1/2) = 1
f(3π/4) = - 2 cos 6π/4 = -2 cos 270 = 0
f(5π/6) = -2 cos 10π/6 = - 2 cos 300 = -2 (1/2) = -1
{-1 , 0 , 1}    (A)